Originally, the existing technology of constructing a puzzle covering a plurality of jigsaw puzzle elements is formed through cutting a jigsaw puzzle board by a set of cutting tools. After division, a plurality of jigsaw puzzle pieces are assembled or matched in such a way that the patterns on the board are recovered or to be formed as the other shapes. In the existing technology, the first side of a jigsaw puzzle board is forced to be cut by the cutting tools to form a plurality of jigsaw puzzle pieces and such a jigsaw puzzle piece having a curved face on the side edge face is formed through the cutting process. However, the sharp edges are often appeared at the second side of the jigsaw puzzle piece due to non-cutting action of the cutting tools. The existence of sharp edges would cause inconvenience to assemble or match two or more jigsaw puzzle pieces, it would also cut the user's hands. In addition, the jigsaw puzzle board cannot be completely cut by the cutting tools during the cutting process. The remaining portion that holds the jigsaw puzzle pieces together are required to be broken up by the user such that the fracturing region of the second side of the jigsaw puzzle pieces easily causes injury to the user.